do these lines intersect?
[x,y,z]=[2,-3,2]+s[3,4,-10]
[x,y,z]=[3,4,-2]+s[-4,5,3]

- anonymous

do these lines intersect?
[x,y,z]=[2,-3,2]+s[3,4,-10]
[x,y,z]=[3,4,-2]+s[-4,5,3]

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- anonymous

Do you want me to show you what I did?

- anonymous

because I'm not getting the answer my book has

- anonymous

alright. lets see what you did

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## More answers

- anonymous

So I made the parametric equations for both lines
line 1 : x=2+3s y=-3+4s z=2-10s line 2: x=3-4t y=4+5t z=-2+3t

- anonymous

Then I set the equations equal to each other. The x of line 1 with the x of like two and so on. I got these 3 equations
3s+4t=1 4s-5t=7 -10s-3t=-4

- anonymous

yep

- anonymous

then I used elimination on 3s+4t=1 and 4s-5t=7. I multiplied 3s+4t=1 by 4 and 4s-5t=7 by 3. I got t=-17/31 after solving

- anonymous

I then subbed t=-17/31 into 4s-5t=7 to find s. I got s=33/31

- anonymous

yep

- anonymous

After getting t and s. I subbed them into -10s-3t=-4 to see if the right side is equal to the left side. I got -9=-4

- anonymous

but my book has an answer but since I'm given x, y and z. the the point of intersection should also have an x y and z in it. but it gives (33/31, -17/31). But those are my s and t values. so I'm a little confused

- anonymous

because the question asks if the intersect, and what the points are if they do

- anonymous

do you think they intersect?

- anonymous

no, because the left side doesn't equal the right side. Also they are not parallel. So I think they are skew lines. But i think i'm wrong

- anonymous

alright. i would have done it a little different to you but here is what i did.

- anonymous

don't both about your s and t values as i chose s and t values for the opposite lines

- anonymous

so yea i got
[3t-4s,4t-5s,-10t-3s]=[1,7,-4]

- anonymous

ok. now here is the thing

- anonymous

i'll say it later, let me get it into parametric form.

- anonymous

so yea your right with parametric form

- anonymous

3t+4s=1 4t-5s=7 -10t-3s=-4

- anonymous

for simplicity sake let X represent 3t+4s=1 Y represent 4t-5s=7 and Z yea u get the drift.

- anonymous

Now for these two lines to intersect, then when solving simultaneously with X and Y these solution should also be the same for when you solve for X and Z or Y and Z
You only need to do either 2 solvings. like say X and Y and X and Z
or X and Y and Y and Z

- anonymous

So you have solutions for X and Y which were t=33/31 and s=-17/31

- anonymous

now for X and Z we get solutions t=13/31 and s=-2/31

- anonymous

since we get totally different solutions for t and s in both scenario's then these lines do not intersect.

- anonymous

to check this we can plug these numbers into
[3t-4s,4t-5s,-10t-3s]=[1,7,-4]
and you will see that you won't get [1,7,-4]

- anonymous

got any queries?

- anonymous

so why does my book give me an answer that is the s and t values. Because before in other question it would just say no and that was all

- anonymous

what do you mean by the s and t values?

- anonymous

the answer my book gives is (33/31, -17/31)

- anonymous

the s and t values i get

- anonymous

thats weird. those values only seem to work of X and Y

- anonymous

either we are wrong or the book is wrong.

- Zarkon

1) double check that you have the question written correctly...2) if you do then the book is wrong

- anonymous

my book always numbers the equations and they always use the first two, x and y then sub into z to see if the sides are equal

- anonymous

i was taught differently. but same concept still applies.

- anonymous

yea so see if you wrote the question down correctly.

- anonymous

yea, i wrote is right

- anonymous

kk. book is silly,

- anonymous

I want to ask my teacher, but i'm scared to say that the book is wrong and i'm right, since i'm just learning this and i'm not the best person in math

- anonymous

doesn't hurt to go through your method with your teacher.

- anonymous

ok. could to stay around. I might have another question

- anonymous

k

- anonymous

I have another question .

- anonymous

My book asks if line r=r(with arrow on top) [-5,1,-2]+k[1,6,5] intersects with the equation [x,y,z]=[2,3,-1]+s[1,3,4]+[-5,4,7]. I know that instead of [x,y,z] i can put r (with arrow on top) but what is with the notation of the first equation, does it mean anything else

- anonymous

can you draw it for me- just the r arrow thing

- anonymous

|dw:1371014894598:dw|

- anonymous

sorry for my bad drawing

- anonymous

thats what it has

- anonymous

thats just a notation for a vector line

- anonymous

so don't get overwhelmed by it. doesn't contribute to your calculations

- anonymous

but why does it have r=r with arrow

- anonymous

i just put it r with arrow = blah blah

- anonymous

because r itself could be a point but since its r dash then this represents vector notation.

- anonymous

ok thank you so much for your help

- Zarkon

You can write vectors on the site
\[\vec{r}\]
\vec{r}

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